The research proposed here involves developing and studying the properties of statistical methodology in survival analysis when some of the data are censored or lost to follow-up. Problems to be attacked fall under two broad categories: (1). General inference problems with censored data; and (ii). sequential inference problems with censored data. Under (i), plans include: problems in survival analysis with dependent censoring patterns; alternatives to two sample tests and estimates in the presence of covariates; estimation of several key functions in survival analysis when data are censored (including the hazard function); an extensive research program in regression models and methods with censored data to attack key problems involving prognostic variables; an adaptive approach to estimation of survival model parameters which is fully efficient; and application to a variety of other general inference problems with censored data. The work planned extends and refines some of the earlier work of this grant, in particular, in the area of regression analysis, and extends to many new areas, e.g., adaptive tests. Such methodology should provide very practical and useful extensions of the survival analysis literature. In addition to the above general inference research in survival methodology, this proposal in (ii) contains a series of problems to be attacked in the area of sequential estimation and testing with censored survival data, including work on curtailed tests. This work is very important for developing statistical methodology in survival studies requiring early decision rules. Such rules are often vitally important form an ethical point of view in clinical trials. Considering the two areas of research proposed, general and sequential inference with censored survival data, the plan incorporates a comprehensive program on statistical methodology useful in survival analysis not currently available, including retrospective and prospective studies.